| First, label points around the unit circle in terms of their fraction around the circle. For example, the point at 90 deg is labeled 1/4, the point at 180 deg is labeled 1/2, and so on. |
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| Next, we use a function D taking numbers in [0, 1] to numbers in [0, 1] defined by |
| D(x) = 2⋅x for 0 ≤ x ≤ 1/2 |
| D(x) = 2⋅x - 1 for 1/2 < x ≤ 1 |
| Notice for example D(1/3) = 2/3 and D(2/3) = 1/3. Together the numbers 1/3 and 2/3 make up a 2-cycle for D(x). |
| Now D(1/7) = 2/7, D(2/7) = 4/7, and D(4/7) = 1/7; D(3/7) = 6/7, D(6/7) = 5/7, and D(5/7) = 3/7. That is, 1/7, 2/7, 4/7 is a 3-cycle for D(X) and 3/7, 6/7, and 5/7 is another 3-cycle. |
| In general, numbers of the form k/(2n - 1) belong to n-cycles for D(x). |
Return to Lavaurs algorithm.